Let's say we have random variable $X$, that is a map $X:Events \rightarrow \mathbb R$. What is the meaning of $$z^X$$ (where z is complex perhaps).
Would I be able to treat X as a real number and say that $$\mathbb E [z^X] = \mathbb E [z(z)...(z)] = \mathbb E[z](\mathbb E[z]) ... (\mathbb E[z]) = (\mathbb E[z])^X$$ ? After all, X is a map onto $\mathbb R$